This gets into something that you and I discussed earlier, that "infinity" can refer to two different concepts. While your interpretation is well-defined, and r

This gets into something that you and I discussed earlier, that "infinity" can refer to two different concepts. While your interpretation is well-defined, and reasonable, it's not what people usually mean when they think of that expression. Even knowing the math and notation behind both of them interpretations and the difference between them, I still tend to see \inf-1 as an ill-defined arithmetic (algebraic) expression rather than a well-defined set operation. Note also, that you can treat \inf as an ordinal number, rather than a cardinal or a limit point, and subtracting one as the inverse of the ordinal successor operation. In this case, \inf-1 has a rigorous definition, which exists almost all of the time, and is somewhat closer to the naive, ill-defined algebraic interpretation. Under this definition, \inf-1 does not equal \inf.